Theorem 7 (Complexity) 
Consider \(\mathsf {T}\)  and \(\mathsf {T}^{\prime }\)  as (possibly infinite) trees \(\mathcal {T}\left(\mathsf {T}\right)\)  and
\(\mathcal {T}\left(\mathsf {T}^{\prime }\right)\)  with asymptotic branching factors \(b\)  and \(b^{\prime }\) 
respectively [1]}, [2]}. Our algorithm has time complexity
\(\mathcal {O}(n\min (b, b^{\prime })^n)\)  and space complexity \(\mathcal {O}(n\min (b, b^{\prime }))\)  in the worst
case to determine if \(\mathsf {T}\le \mathsf {T}^{\prime }\)  with bound \(n\) .

